Group #23771108 — subgroups

Subgroups — #23771108

Order 10112.

428 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19098480	C₂	1	3	yes	maximal
2	#19098474	C₂	1	2	yes	maximal, complemented
3	#19098455	C₂	1	6	yes	maximal, complemented
4	#19098428	C₂	1	3	yes	maximal, complemented
5	#395×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₃₁₆	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊Dic₇₉	C₂²	1	3	yes	—
8	C₂×(C₂×D₇₉)⋊C₄	C₂²	1	6	yes	—
9	C₂×(C₂×D₇₉)⋊C₄	C₂²	1	6	yes	—
10	C₂×C₄×Dic₇₉	C₂²	1	3	yes	—
11	C₇₉⋊#95	C₂²	1	3	yes	—
12	C₇₉⋊#95	C₂²	1	6	yes	—
13	C₂²×Q₈×C₇₉	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊C₄×C₇₉	C₂²	1	3	yes	—
15	#95×C₇₉	C₂²	1	3	yes	—
16	C₂³×D₇₉	C₂³	1	2	yes	—
17	C₂×D₃₁₆	—	4	3	no	—
18	C₂²×Dic₇₉	C₂³	1	6	yes	—
19	C₄⋊Dic₇₉	—	4	3	no	—
20	(C₂×D₇₉)⋊C₄	—	2	12	no	—
21	(C₂×D₇₉)⋊C₄	—	4	6	no	—
22	C₄×Dic₇₉	—	2	6	no	—
23	C₂×Q₈×C₇₉	—	4	3	no	—
24	C₂²×C₄×C₇₉	C₂³	1	3	yes	—
25	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
26	C₂²×C₄×C₇₉	C₂³	1	3	yes	—
27	C₄⋊C₄×C₇₉	—	4	3	no	—
28	C₂³×C₇₉	C₂⁴	1	1	yes	characteristic
29	C₂²×D₇₉	—	2	6	no	—
30	C₂²×D₇₉	—	2	6	no	—
31	C₂²×D₇₉	—	2	2	no	—
32	Q₈×C₇₉	—	4	4	no	—
33	C₂×C₄×C₇₉	—	2	3	no	—
34	C₂×C₄×C₇₉	—	2	3	no	—
35	C₂×C₄×C₇₉	—	2	6	no	—
36	C₂×C₄×C₇₉	—	2	3	no	—
37	C₂×C₄×C₇₉	—	2	3	no	—
38	C₂×C₄×C₇₉	#41	1	6	yes	—
39	C₂×Dic₇₉	—	2	6	no	—
40	C₂×Dic₇₉	—	2	6	no	—
41	C₂×Dic₇₉	—	2	6	no	—
42	D₃₁₆	—	4	4	no	—
43	C₂²×C₇₉	C₂×#41	1	3	yes	—
44	C₂²×C₇₉	H(5,𝔽₂)	1	3	yes	—
45	C₂²×C₇₉	2₋¹⁺⁴	1	1	yes	characteristic
46	C₂×D₇₉	—	4	6	no	—
47	C₂×D₇₉	—	4	6	no	—
48	C₂×D₇₉	—	4	2	no	—
49	C₄×C₇₉	—	2	6	no	—
50	C₄×C₇₉	—	4	3	no	—
51	C₄×C₇₉	—	4	1	no	—
52	Dic₇₉	—	4	6	no	—
53	C₂×C₇₉	#539	1	3	yes	—
54	C₂×C₇₉	#555	1	3	yes	—
55	C₂×C₇₉	H(3,𝔽₄)	1	1	yes	characteristic
56	D₇₉	—	8	2	no	—
57	#2785	—	79	1	no	maximal, Sylow
58	C₇₉	#2785	1	1	yes	characteristic, complemented, Sylow
59	#395	D₇₉	1	1	yes	characteristic, complemented
60	#394	—	79	3	no	—
61	#393	—	79	2	no	—
62	#388	—	79	6	no	—
63	#382	—	79	3	no	—
64	C₂²×Q₈	C₂×D₇₉	1	1	yes	characteristic
65	C₂²×D₄	—	79	1	no	—
66	C₂×C₄⋊C₄	—	79	3	no	—
67	C₂×C₄⋊C₄	C₂×D₇₉	1	3	yes	—
68	C₂×C₂²⋊C₄	—	79	6	no	—
69	C₂×C₂²⋊C₄	—	79	6	no	—
70	C₂×C₄²	—	79	3	no	—
71	#95	—	79	3	no	—
72	#95	—	79	6	no	—
73	#95	C₂×D₇₉	1	3	yes	—
74	C₂⁴	—	79	2	no	—
75	C₂×Q₈	—	4	3	no	—
76	C₂×D₄	—	316	3	no	—
77	C₂²×C₄	—	79	6	no	—
78	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
79	C₂²×C₄	C₂²×D₇₉	1	3	yes	—
80	C₂²×C₄	C₂²×D₇₉	1	3	yes	—
81	C₄⋊C₄	—	4	3	no	—
82	C₄⋊C₄	—	316	3	no	—
83	C₂²⋊C₄	—	316	6	no	—
84	C₂²⋊C₄	—	158	12	no	—
85	C₄²	—	158	6	no	—
86	C₂³	—	158	6	no	—
87	C₂³	—	158	6	no	—
88	C₂³	—	158	2	no	—
89	C₂³	C₂³×D₇₉	1	1	yes	characteristic
90	Q₈	—	4	4	no	—
91	D₄	—	316	4	no	—
92	C₂×C₄	—	2	3	no	—
93	C₂×C₄	—	2	3	no	—
94	C₂×C₄	—	2	6	no	—
95	C₂×C₄	—	2	3	no	—
96	C₂×C₄	—	2	3	no	—
97	C₂×C₄	—	158	6	no	—
98	C₂×C₄	—	158	6	no	—
99	C₂×C₄	—	158	6	no	—
100	C₂×C₄	#11929625	1	6	yes	—
101	C₂²	—	316	6	no	—
102	C₂²	—	316	6	no	—
103	C₂²	—	316	2	no	—
104	C₂²	C₂×#11929625	1	3	yes	—
105	C₂²	#14579206	1	3	yes	—
106	C₂²	#14579208	1	1	yes	characteristic
107	C₄	—	2	6	no	—
108	C₄	—	4	1	no	—
109	C₄	—	4	3	no	—
110	C₄	—	316	6	no	—
111	C₂	—	632	2	no	—
112	C₂	#19099162	1	3	yes	—
113	C₂	#19099279	1	3	yes	—
114	C₂	#19099306	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19098480

C₂

yes

maximal

#19098474

C₂

yes

maximal, complemented

#19098455

C₂

yes

maximal, complemented

#19098428

C₂

yes

maximal, complemented

#395×C₇₉

C₂

yes

maximal, characteristic, complemented

C₂²×D₃₁₆

C₂²

yes

characteristic

C₂×C₄⋊Dic₇₉

C₂²

yes

—

C₂×(C₂×D₇₉)⋊C₄

C₂²

yes

—

C₂×(C₂×D₇₉)⋊C₄

C₂²

yes

—

C₂×C₄×Dic₇₉

C₂²

yes

—

C₇₉⋊#95

C₂²

yes

—

C₇₉⋊#95

C₂²

yes

—

C₂²×Q₈×C₇₉

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₇₉

C₂²

yes

—

#95×C₇₉

C₂²

yes

—

C₂³×D₇₉

C₂³

yes

—

C₂×D₃₁₆

—

C₂²×Dic₇₉

C₂³

yes

—

C₄⋊Dic₇₉

—

(C₂×D₇₉)⋊C₄

—

(C₂×D₇₉)⋊C₄

—

C₄×Dic₇₉

—

C₂×Q₈×C₇₉

—

C₂²×C₄×C₇₉

C₂³

yes

—

C₂²×C₄×C₇₉

C₂³

yes

characteristic

C₂²×C₄×C₇₉

C₂³

yes

—

C₄⋊C₄×C₇₉

—

C₂³×C₇₉

C₂⁴

yes

characteristic

C₂²×D₇₉

—

C₂²×D₇₉

—

C₂²×D₇₉

—

Q₈×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

#41

yes

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

D₃₁₆

—

C₂²×C₇₉

C₂×#41

yes

—

C₂²×C₇₉

H(5,𝔽₂)

yes

—

C₂²×C₇₉

2₋¹⁺⁴

yes

characteristic

C₂×D₇₉

—

C₂×D₇₉

—

C₂×D₇₉

—

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

—

Dic₇₉

—

C₂×C₇₉

#539

yes

—

C₂×C₇₉

#555

yes

—

C₂×C₇₉

H(3,𝔽₄)

yes

characteristic

D₇₉

—

#2785

—

maximal, Sylow

C₇₉

#2785

yes

characteristic, complemented, Sylow

#395

D₇₉

yes

characteristic, complemented

—

—

—

—

C₂²×Q₈

C₂×D₇₉

yes

characteristic

C₂²×D₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₇₉

yes

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₄²

—

#95

—

#95

—

#95

C₂×D₇₉

yes

—

C₂⁴

—

C₂×Q₈

—

C₂×D₄

—

316

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₇₉

yes

characteristic

C₂²×C₄

C₂²×D₇₉

yes

—

C₂²×C₄

C₂²×D₇₉

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

316

—

C₂²⋊C₄

—

316

—

C₂²⋊C₄

—

158

—

C₄²

—

158

—

C₂³

—

158

—

C₂³

—

158

—

C₂³

—

158

—

C₂³

C₂³×D₇₉

yes

characteristic

Q₈

—

D₄

—

316

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

158

—

C₂×C₄

—

158

—

C₂×C₄

—

158

—

100

C₂×C₄

#11929625

yes

—

101

C₂²

—

316

—

102

C₂²

—

316

—

103

C₂²

—

316

—

104

C₂²

C₂×#11929625

yes

—

105

C₂²

#14579206

yes

—

106

C₂²

#14579208

yes

characteristic

107

C₄

—

108

C₄

—

109

C₄

—

110

C₄

—

316

—

111

C₂

—

632

—

112

C₂

#19099162

yes

—

113

C₂

#19099279

yes

—

114

C₂

#19099306

yes

characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₇₉
commutator, socle, cosocle	C₂³×C₇₉	C₂⁴
Fitting	#395×C₇₉	C₂
prime radical	C₂²×D₃₁₆	C₂²
hypercenter	#395	D₇₉
hypocenter	C₇₉	#2785
LCS	G ▷ C₂³×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ #395

subgroup

G/H

center, Frattini

C₂³

C₂³×D₇₉

commutator, socle, cosocle

C₂³×C₇₉

C₂⁴

Fitting

#395×C₇₉

C₂

prime radical

C₂²×D₃₁₆

C₂²

D₇₉

C₇₉

G ▷ C₂³×C₇₉ ▷ C₇₉

C₁ ◁ C₂³ ◁ #395

N	H ≅ G/N	type
2. #19098474	C₂	semidirect
3. #19098455	C₂	semidirect
4. #19098428	C₂	semidirect
5. #395×C₇₉	C₂	semidirect
58. C₇₉	#2785	semidirect
59. #395	D₇₉	semidirect

H ≅ G/N

type

2. #19098474

C₂

semidirect

3. #19098455

C₂

semidirect

4. #19098428

C₂

semidirect

5. #395×C₇₉

C₂

semidirect

58. C₇₉

#2785

semidirect

59. #395

D₇₉

semidirect

Subgroups — #23771108

Conjugacy classes of subgroups

Complements